MU03258 Geometric Theory of Partial Differential Equations I

Mathematical Institute in Opava
Winter 2019
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: z (credit).
Teacher(s)
prof. RNDr. Artur Sergyeyev, Ph.D., DSc. (lecturer)
Guaranteed by
prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava
Prerequisites
( MU02037 Partial Differential Equations || MU03035 Partial Differential Eq. II || MU03135 Partial Differential Eq. II ) && TYP_STUDIA ( N )
MU/02024, MU/02027, MU/03038
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
In this course we will become acquainted with a number of modern methods for solving differential equations which are "located" at the intersection of geometry of the so-called jet spaces and theory of Lie groups and Lie algebras. Successful completion of this course requires good knowledge of standard theory of ordinary and partial differential equations and of differential geometry.
Syllabus
  • The jet spaces, total derivatives, prolongation of differential equations.
    Point transformations, infinitesimal symmetries and their computation.
    Integration of ODEs and reduction using symmetries. Invariant solutions.
    Higher (generalized) symmetries. Evolutionary derivations and evolutionary form of a higher symmetry. The Lie bracket of symmetries. Point and contact symmetries as special cases of higher symmetries.
Literature
    recommended literature
  • A.M. Vinogradov, I.S. Krasil'ščik, eds. Simmetrii i zakony sochraneniya uravnenij matematičeskoj fiziki. Faktorial, Moskva, 1997. info
  • P. J. Olver. Applications of Lie groups to differential equations. Springer, New York, 1993. info
  • G. W. Bluman a S. Kumei. Symmetries and Differential Equations. Springer, New York, 1989. info
    not specified
  • C. Rogers a W. F. Shadwick. Bäcklund transformations and Their Applications. Academic Press, New York, 1982. info
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
Attending the lectures is desirable. In the course of the first lecture the lecturer will communicate to the students the requirements regarding the conditions of successfully passing the subject. Succeeding in the fail/pass test requires attaining the score of at least 60 percent at the test papers (typically two in the semester) or 70 percent at the remedial test paper. The exact requirements and dates for submitting the papers are set by the tutor. The exam is merely oral. In its course one tests the knowledge and the skills of the students gained during the study of the subject in question.
The course is also listed under the following terms Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018.
  • Enrolment Statistics (recent)
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